Question

A test of a driver’s perception/reaction time is being conducted on a special testing track with wet pavement and a driving speed of 65 mi/h. when the driver is sober, a stop can be made just in time to avoid hitting an object that is first visible 555 ft a head. After a few drinks under the exact same conditions, the driver fails to stop in time and strikes the object at a speed of 35 mi/h.

Question - 6 Determine the Braking distance for sober driver?

Question - 7 Determine the sober driver perception-reaction distance?

Question - 8 Determine the sober driver's perception/reaction time?

Question - 9 Determine the perception/reaction time of driver after drinking?

Answer 1

Given :- • Driving speed (v1) = 65 mi/hr

• The velocity of drinking driver when the vehicle strikes the object under the same condition, (v2) = 35 mi/hr

• Total stopping distance of vehicle when driver is sober to avoid collision with the object (ds) = 555 ft

Solution:- The whole solution is shown in below images.

We know, 1 mi = 5280 ft

So, driving distance (V1) = ( 65 × 5280 ) / ( 3600 ) = 95.333 ft/s

And, velocity of drinking driver after the vehicle strikes the object, (V2) = ( 35 × 5280 ) /( 3600 ) = 51.333 ft/s

Acceleration due to gravity, g = 32.2 ft/s^2

Coefficient of friction of wet pavement, f = 0.35

Part (6) :- The braking distance for sober driver (d) can be calculated using the formula:- d = (V1)^2 / (2 g f)

Substitute the respective values in order to get the braking distance. The required braking distance (d) for sober driver is obtained as 403.21 ft.

Part (7) :- Total stopping distance (ds) is the sum of perception-reaction distance (dr) and braking distance (d).

So, ds = dr + d

So, 555 ft = dr + 403.21 ft

Hence, dr = 151.79 ft.

Therefore, the required perception-reaction distance (dr) of sober driver is 151.79 ft.

Part (8) :- Perception- reaction distance is equal to the multiplication of driving speed (V1) with the perception reaction time (tr).

dr = (V1) × (tr)

So, tr = dr / V1 = (151.79 / 95.333) = 1.592 sec

Therefore, the sober driver's perception reaction time (tr) is 1.592 sec.

Part (9) :- Total stopping distance of driver after drinking is equal to the sum of perception reaction distance of driver after drinking and braking distance of driver after drinking.

So, ds = ( V1 × t) + [ { (V1)^2 - (V2) ^2 } / ( 2 × g × f ) ]

Substitute all respective values to get the value of perception reaction time (t).

The perception reaction time (t) of driver after drinking is obtained as 2.818 sec.